CAIE A-Level Physics A2 20.5 Electromagnetic Induction Questions

Practise defining and calculating magnetic flux and flux linkage, explaining induction experiments, and applying Faraday’s and Lenz’s laws to induced e.m.f. and direction.

Exam points

define, calculate and interpret magnetic flux, flux linkage and Phi=BA
describe induction experiments and explain changing flux linkage
apply Faraday and Lenz laws to calculate induced emf and determine its direction

Covered syllabus points

20.5.1—Magnetic flux as the product of the magnetic flux density and the 20.5.2—Φ = BA 20.5.3—The concept of magnetic flux linkage 20.5.4—Experiments that demonstrate: • that a changing magnetic flux can induce an 20.5.5—Faraday’s and Lenz’s laws of electromagnetic induction

[Maximum number: 11]

(a)

Define magnetic flux.

[ 2 ]

(b)

A square coil of wire of side length 12 cm consists of 8 insulated turns. The coil is stationary in a uniform magnetic field. The plane of the coil is perpendicular to the magnetic field, as shown in Fig. 6.1.

Fig. 6.1

The flux density B of the magnetic field varies with time t as shown in Fig. 6.2.

Fig. 6.2

[ 6 ]

(i)

Determine the magnetic flux linkage inside the coil at time $t=0.60 \mathrm{~s}$ . Give a unit with your answer.

magnetic flux linkage =unit.............. [3]

[ 3 ]

$N \Phi=B A N$ $=400 \times 10^{-3} \times 0.12^{2} \times 8$ $=0.046 \mathrm{~Wb}$

(ii)

State how Fig. 6.2 shows that the electromotive force (e.m.f.) E induced across the terminals between t=0 and $t=0.60 \mathrm{~s}$ is constant.

[ 1 ]

(iii)

Calculate the magnitude of E.

\begin{aligned} & E= \\ & \text { V [2] } \end{aligned}

[ 2 ]

(induced) e.m.f. = rate of change of flux linkage
$\begin{aligned} \text { e.m.f. } =N \Phi / t =0.046 / 0.60 =0.077 \mathrm{~V} \end{aligned}$

(c)

The procedure in (b) is repeated, but this time the terminals of the coil are connected together.

State and explain the effect on the coil of connecting the terminals together during the change of magnetic flux density shown in Fig. 6.2.

[ 3 ]

[Maximum number: 14]

(a)

State Faraday's law of electromagnetic induction.

[ 2 ]

(b)

Fig. 7.1 shows a coil at rest in a uniform magnetic field that is parallel to the axis of the coil.

Fig. 7.1

The coil is connected to a centre-zero voltmeter.

The flux density B of the uniform magnetic field varies with time t as shown in Fig. 7.2.

Fig. 7.2

The coil consists of 340 turns, each of cross-sectional area $3.2 \times 10^{-4} \mathrm{~m}^{2}$ .

[ 12 ]

(i)

Calculate the maximum magnetic flux through one turn of the coil.
maximum magnetic flux = Wb

Figure for Question (i) — CAIE A-Level Physics A2

[ 2 ]

$\begin{aligned} \Phi =B A =7.2 \times 10^{-3} \times 3.2 \times 10^{-4} =2.3 \times 10^{-6} \mathrm{~Wb} \end{aligned}$

(ii)

Determine the maximum rate of change of magnetic flux linkage in the coil.
maximum rate of change of flux linkage = $\mathrm{Wbs}^{-1}$

[ 3 ]

tangent drawn at steepest point on Fig. 7.2
evidence of multiplication by 340
Marking guidance:

maximum rate of change of flux $=0.82 \mathrm{~Wb} \mathrm{~s}^{-1}$

(iv)

Fig. 7.3

[ 3 ]

sinusoidal curve of period 2.0 ms from t=0 to t=6.0 ms

all peaks at

+V_0

and all troughs at

-V_0

line showing

V=0

at (and only at) t=0, 1.0, 2.0, 3.0, 4.0, 5.0 and 6.0 ms

(v)

V=A\sin Bt

A=\underline{\hspace{3cm}}\ \mathrm{V}\qquad B=\underline{\hspace{3cm}}\ \mathrm{rad\,s^{-1}}

[ 3 ]

A=0.82\ \mathrm{V}

or A has same numerical value as answer in (b)(iii), with unit V

B=\frac{2\pi}{2.0\times10^{-3}}

=3100\ \mathrm{rad\,s^{-1}}

[Maximum number: 8]

(a)

A small coil C has 64 turns and cross-sectional area $0.71 \mathrm{~cm}^{2}$ . The coil is placed inside a solenoid as shown in Fig. 6.1.

Fig. 6.1

The centre of coil C is on the central axis of the solenoid.

[ 8 ]

(i)

There is a constant current in the solenoid.

Coil C is moved through the solenoid from position X to position Y .
On Fig. 6.2, sketch a line to show the variation of the magnetic flux linkage in coil C with position as it moves from X to Y .

Fig. 6.2

[ 1 ]

(ii)

Explain the shape of your line in (a)(i).

[ 2 ]

constant flux density (inside coil)
either (magnetic) flux linkage proportional to flux density

or $\quad \Phi=B A N$ and B, A and N are all constant

(iii)

Coil C is now held stationary at X . The current in the solenoid varies so that the magnetic flux density B at X varies from time 0 to time 4 t as shown in Fig. 6.3.

Fig. 6.3

Calculate the maximum magnetic flux linkage in coil C .
flux linkage = Wb

[ 2 ]

$\Phi=B A N$ $\begin{aligned} =0.080 \times 0.71 \times 10^{-4} \times 64 =3.6 \times 10^{-4} \mathrm{~Wb} \end{aligned}$

(iv)

On Fig. 6.4, sketch a line to show the induced electromotive force (e.m.f.) E in coil C from time 0 to time 4 t.

Fig. 6.4

[ 3 ]

[Maximum number: 2]

Define magnetic flux.

[Maximum number: 2]

Fig. 7.1 shows a coil at rest in a uniform magnetic field that is parallel to the axis of the coil.

Fig. 7.1

The coil is connected to a centre-zero voltmeter.

The flux density B of the uniform magnetic field varies with time t as shown in Fig. 7.2.

Fig. 7.2

The coil consists of 340 turns, each of cross-sectional area $3.2 \times 10^{-4} \mathrm{~m}^{2}$ .

Calculate the maximum magnetic flux through one turn of the coil.
maximum magnetic flux = Wb

Figure for Question 5 — CAIE A-Level Physics A2

$\begin{aligned} \Phi =B A =7.2 \times 10^{-3} \times 3.2 \times 10^{-4} =2.3 \times 10^{-6} \mathrm{~Wb} \end{aligned}$

[Maximum number: 5]

A capacitor of capacitance $470 \mu \mathrm{~F}$ is connected to a battery of electromotive force (e.m.f.) 24 V in the circuit of Fig. 5.1.

Fig. 5.1

The two-way switch S is initially at position X.
P and Q are identical long straight wires, each with a resistance of $5.6 \mathrm{k} \Omega$ . These wires are placed near to, and parallel to, each other. Wire Q is connected to a voltmeter.

At time t=0, switch S is moved to position Y so that the capacitor discharges through wire P .

(a)

Explain why there is an induced e.m.f. across wire Q during the discharge of the capacitor.

[ 3 ]

(b)

On Fig. 5.3, sketch a line to suggest the variation with t of the voltmeter reading V.

Fig. 5.3

[ 2 ]

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (c)

Question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question (v)

Question 3

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question 4

Question 5

Question 6

Question (a)

Question (b)